Oh Tu Ri: Numbering in music
Matt Berkley
Draft
23 October 2004, revised 24 October
Here is a way I've begun to think about pitch in music, and guitar tunings, and chords. I think it helps my musical ear. Maybe it will be useful for other people as well. At the end are some sketchy ideas about counting.
What follows relates to Western-style 12-tone scales.
This is an early draft so I expect to have included mistakes.
Contents
1. Note names: T and L
2. Intervals and chords: the Two Chord
3. String instrument tunings: 070470
4. Counting beats: 4321
1. Note names
I've started thinking in chromatic numbering, like on guitar frets - numbering the notes in order upwards with 0 as the root.
"Three Blind Mice" starts on frets 4,2,0.
So I can sing "Four two oh".
I like having the root as 0 because the intervals are clear.
The chromatic Do-re-mi could be:
"Oh Two Three Four Five Six Sev Eight Nine Ten Lev".
Major scale could be:
"Oh Two Four Five Sev Nine Lev Oh".
I did devise something with shorter names:
"Oh Tu Ri Fo Fa Si Se Ey Na Te Le"
but now I think it's easier to start with the numbers and shorten as I get used to the system.
For writing or typing the numbers, if the spacing of "11" and "12" causes problems when typed, T and L can be used for Ten and Leven.
So we get a Western chromatic scale of 0123456789TL
and a Western major scale of 024579L .
Arabic-type scale: 014578T .
"Happy birthday" starts on
77970L
What about the fact that in the tune, the 0 and L are higher in pitch than the rest of the notes?
Well, we could try something like _0 for lower notes, and ^0 for higher notes.
7797^0L
Or
7 7 9 7 12 11 .
Another possibility:
-------------------------
0
L
9
7 7 7
-------------------------
For simple tunes that I already know, the simple system 77970L is enough.
Ah. Here's another idea.
0
7797 L
2. Intervals
I think it would improve my ear if I trained myself to think in chromatic-step terms for intervals: seven frets up, and so on.
To get from a G to the next G up, a chord/arpeggio can be
0470 (remember 0 takes the place of 12).
This shows us that the first interval is 4, then we go up 3 more to get to 7, then 5 more to get to 0.
Try playing or singing the broken chord/scale 03690.
Try 0480, 047T, 047T2, 047L.
Naming chords
Since we only need to mention notes other than the root, we can notate chords like this:
C47
which is the same number of syllables as "C major".
One advantage of the C47 system is that if we sing the name of the chord, we've already sung the broken chord.
Sevnnn!"
Four
"Cee
Since when naming chords we can often leave out the root and the seventh note up, we might notate chords like this:
C3T (C Three Ten).
It's interesting to sing these as broken chords, or just imagine what they are going to sound like before we play them, because we're more used to other sequences like major scales.
For me it is not as intuitive as I thought to sing the sequence C3T. That makes me think it's good mental exercise.
Tip in case of difficulty finding the tenth note
Either a) go up seven notes from the 3 note
(remember 7 is an important interval and should be easy to find: if you can't find the 7th note up from another note practise finding the 12th note up or down, then move on to 7th notes, then to other intervals).
or b) go to the 12th note up (0h) and go to the next bluesy note down (Ten).
I quite like the idea of calling chords things like the
Two chord (short for a 4-Ten-Two chord, 047T2),
the
Leven chord (short for the 4-Eleven chord 047L),
the
Three-Six-Nine chord and
the
Four-Eight chord.
An
Oh-Sevn is a ringing chord with no other notes.
A
Three chord is the one that people say sounds sad.
String instruments and chords
On the piano, many-fingered chords 036903, 047TL and so on are easy to work out and play; on the guitar they're harder to find and harder to play.
For ear-training purposes, the notes are easy to find on one string. If there's no string available for the key, we can first try finding the notes on one of the strings. The idea is to get used to knowing what the intervals, multiple intervals (chords and scales) and chords will sound like, as a prelude to making the sounds we want to make.
Often it's good to leave out some notes in a chord and just imply them. Once we know where the notes are (see below) we can try different combinations. [Below are ideas for numbers in tunings: this gives the notes for open strings and a starting point for finding notes for chords anywhere on the neck].
An idea for notating chord progressions
It might be preferable in some cases to leave the note numbers unchanged even when the chord changes (provided the whole feel of the piece doesn't modulate).
So for a blues in C, say we start in 047T (C,E,G,Bb).
We could notate the F chord by something like F047T (i.e. F,A,C,Eb).
Or we could just write 5903 (If we keep C as the 0, then 5903 gives F,A,C,Eb).
I like this idea because it's easy to see as a sequence on a guitar fretboard using one string, or a piano. Playing chords as broken chords on one guitar string is quite nice.
3. String instrument tunings
Tunings can be written with any note as the root 0, so really there are 12 ways of notating them.
I've used the chromatic system to try and understand open tunings more easily.
These examples are for guitar. With the most obvious note as the root in each case:
Open D 070470
Open G 707047
Open C 070704
Players of open string tunings know that moving across one string transfers chord shapes across the tunings. If we look at the numbers above it's easy to see the principle: look at the diagonal pattern of 7s, 0s and 4s.
EADGBE tuning, if you play in G, yields a root on the G string:
EADGBE
927049
^^^
Note the 704 (DGB). Hopefully it's easy for learners to see that chord shapes and melodies on those strings can be transferred to:
Open D 070470
^^^
Open G 707047
^^^
Open C 070704
^^^
and that a 4-string 0704 pattern is repeated in those three tunings.
What this system does very well is to show relationships between tunings.
BF#BD#F#B |
CGCEGC |
DADF#AD | are all 070470.
EBEG#BE |
etc. |
Let's look at some tunings where Ds are numerous:
DADEAD 070270
Open Dm 070370
Open D 070470
DADGAD 070570
etc.
It's worth bearing in mind that we can describe the tunings by reference to any of the 12 notes in the scale.
EADGBE
in E 05T370
in A 705T27
etc.
The good thing is that we can relate tunings to each other by renumbering. Some open tunings may sound better played in a key that's not so obvious.
In numbering notes, remember you are in base 12, not in base 10.
Think of hours of the day if that makes it easier (i.e. 7+5=0; 7+7=2).
Finding notes
Suppose I'm in "open C" tuning. One nice thing is that I can immediately see from the numbers, while holding the guitar, some easy options. Let's look at the tuning.
070704
To find more notes of a C chord, all I need to do is find other 7s,4s and 0s.
I look
070704
and visualise the fretboard while I look
or perhaps better, sing the notes internally or externally
or both
and see or hear, for instance, that strumming while fretting 004000 will still give a C chord.
A boogie pattern can be on notes 7 and 9, so I can use the existing 7s in the tuning 070704 and the second fret.
Finding a boogie pattern
I can look at the tuning
070704
and meanwhile feel for strings 5 and 3 (the sevens) and play shuffle on the noughth and second fret of both.
000000 to 020020, or x0xx0x to x2xx2x or something in between.
Or use noughth, second and third frets, or frets 0,2,3,5, or descending 5,3,2,0.
Finding chords
Example: A suspended chord (C with an F in it) is easy to see:
Look at the tuning
070704
I want a 5 note so I fret 000001.
If I want to put the 4 note back in, I can fret 004001, without having the 4 and the 5 next to each other in pitch.
Damping to get chords
I can damp strings and strum to get a partial G chord x7x7x4 (in my terminology a G9). and then a very partial C "chord" 0x0x0x (or can do 0x0x04).
By doing a few minutes of this damping I realised how useful it is for strumming. It's possible sometimes to suggest chords by just resting the fingers on the strings I want to damp.
Note to self: Idea for a tuning:
CGCACE
Down one fret
BF#BG#BD#
i.e.
070904
4. Counting beats in music
I've also tried different ways of counting:
a) 0123 instead of 1234. Think of the first note of the bar as the main note and the others as echoes.
b) 4321. Since the 4 is a bigger number, it seems more natural to have this as the main note.
c) Blend of both methods: 3210.
d) Cha-one-two-three Cha-one-two-three. Can put any syllable in place of the Cha.
e) Cha-two-one-oh.
More experiments needed.
-----------------------------
Contact information:
Matt Berkley
33 Howard St
Oxford
OX4 3AY
+44 (0)1865 726768
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